GCF of 294/219, 2352/2329
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 294/219, 2352/2329 i.e 294/510051 easily. The following is the detailed procedure to determine the greatest common factor of fractions 294/219, 2352/2329.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 294/219,2352/2329?
Given fractions are 294/219,2352/2329
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 294/219,2352/2329, numerators are 294,2352
Denominators are 219,2329
The GCF of 294,2352 is 294 .
LCM of 219,2329 is 510051.
The greatest common factor of 294/219,2352/2329 = [GCF of 294,2352]/[LCM of 219,2329]= 294/510051
Therefore, the GCF of 294/219,2352/2329 is 294/510051.
To find the highest common factor of 294,2352, we have to find the factors of both numbers and list the highest common factor.
The factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294
The factors of 2352 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 49, 56, 84, 98, 112, 147, 168, 196, 294, 336, 392, 588, 784, 1176, 2352
The HCF of 294,2352 is 294.
Lets's calculate GCF of 294,2352
| 2 | 294, 2352 |
| 3 | 147, 1176 |
| 7 | 49, 392 |
| 7 | 7, 56 |
| 1, 8 |
∴ So the GCF of the given numbers is 2 x 3 x 7 x 7 = 294
Greatest Common Factor of 294,2352 By Matching Biggest Common Factor Method
Now, list down the factors of 294
:1,2,3,6,7,14,21,42,49,98,147,294
Now, list down the factors of 2352
:1,2,3,4,6,7,8,12,14,16,21,24,28,42,48,49,56,84,98,112,147,168,196,294,336,392,588,784,1176,2352
Greatest Common Factor
We found the factors 294,2352 . The biggest common factor number is the GCF number.
So the greatest common factor 294,2352 is 294.
Lets's calculate LCM of 219,2329
Given numbers has no common factors except 1. So, there LCM is their product i.e 510051
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 294/510051
Therefore, the GCF of Fractions 294/219,2352/2329 is 294/510051
Least Common Multiple of 219,2329 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 219,2329 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(219,2329) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(219,2329) x common factors =1 x 1 = 1
LCM(219,2329) = ( 219 × 2329 ) / 1
LCM(219,2329) = 510051 / 1
LCM(219,2329) = 510051
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FAQs on GCF of Fractions of 294/219, 2352/2329
1. What is the HCF of 294,2352?
The HCF of 294,2352 is 294
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 294/219, 2352/2329?
Answer: GCF of Numerators as per given numbers 294/219, 2352/2329 is
GCF of Numerators i.e. for 294,2352 is 294
LCM of denominators i.e. for 219,2329 is 510051.
Thus, GCF of Fractions is 294/510051.Finally, GCF of Fractions for 294/219, 2352/2329 is 294/510051.